هذه ركلة جزاء.

Because ركلة is a feminine singular noun, and the demonstrative has to agree with it.

• هذا = this for masculine singular
• هذه = this for feminine singular

ركلة ends in ة (tāʾ marbūṭa), which is a very common sign that a noun is grammatically feminine. So Arabic uses هذه ركلة...

In Arabic, the present-tense is / am / are is usually not spoken or written in simple sentences like this.

So:

• هذه ركلة جزاء
  literally: this penalty-kick
• natural English meaning: This is a penalty kick

This kind of sentence is called a nominal sentence in Arabic.

Yes, it is one phrase: ركلة جزاء is a noun phrase meaning penalty kick.

It is built as an iḍāfa (construct phrase), which is very common in Arabic.

• ركلة = kick
• جزاء = penalty / punishment

So literally it is something like a kick of penalty, but in natural English that becomes a penalty kick.

Arabic often uses this noun + noun structure where English might use:

• an adjective
• another noun used like an adjective
• an of phrase

Because ركلة is the first word in an iḍāfa, and the first word of an iḍāfa:

• does not take ال
• does not take tanwīn

So you do not say:

• الركلة جزاء
• ركلةٌ جزاء

Instead, you say:

• ركلةُ جزاءٍ with full case endings
• or simply ركلة جزاء in normal unvowelled writing

Its definiteness depends on the second noun:

• ركلة جزاء = a penalty kick
• ركلة الجزاء = the penalty kick

No. جزاء is a noun, not an adjective.

That matters because an Arabic adjective would normally agree with the noun in:

• gender
• number
• definiteness
• case

But جزاء does not do that here. Instead, it is the second noun in an iḍāfa: ركلة جزاء.

So this is not noun + adjective. It is noun + noun.

Because ركلة has tāʾ marbūṭa (ة).

When a word with ة is said by itself or at a pause, it often sounds like -a or -ah. But when it is grammatically connected to what follows, especially in an iḍāfa, it is pronounced as t.

So:

• by itself: ركلة ≈ raklah
• in this phrase: ركلة جزاء ≈ raklat jazāʾ
• with full case endings: raklatu jazāʾin

In fully vowelled, careful Modern Standard Arabic, it would be:

هذه ركلةُ جزاءٍ.

Here is why:

• هذه = demonstrative, unchanged here
• ركلةُ = nominative, because it is the predicate of the sentence
• جزاءٍ = genitive, because it is the second term of the iḍāfa

In normal Arabic writing, these short vowel endings are usually left out, so you normally see:

هذه ركلة جزاء.

No. هذه ركلة جزاء is already complete and correct.

Arabic does not need an extra pronoun here. هذه already does the job of this.

You may sometimes see هي added in other sentences for emphasis or clearer identification, especially when both parts of the sentence are definite. But in this basic sentence, هذه ركلة جزاء is the normal form.

Here, هذه is functioning as a demonstrative pronoun meaning this.

It is the first part of the sentence, and ركلة جزاء is what is being said about it.

So the structure is basically:

• هذه = this
• ركلة جزاء = a penalty kick

Together: This is a penalty kick.

If the sentence were instead something like هذه الركلة, then هذه would be part of a noun phrase meaning this kick. But in هذه ركلة جزاء, it is the subject of the sentence.